Consider the family of lines and . If the lines of these two families intersect at right angles to each other, then the locus of their point of intersection is a circle with radius
If all the lines of are intersecting the lines of in right angle, then the locus of the point of intersection is a circle, whose diameter end points are points of intersections of both family of lines.
The point of intersection of the lines is and the point of intersection of the lines is
Therefore, the radius of the locus of point of intersection is half of the distance between the points and
Hence, the radius .
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